Related papers: Enhancing Population Persistence by a Protection Z…
We consider a nonlocal bistable reaction-diffusion equation, which serves as a model for a population structured by a phenotypic trait, subject to mutation, trait-dependent fitness, and nonlocal competition. Within this replicator-mutator…
We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different…
The survival of populations hinges on their ability to offset local extinctions through new colonizations. The dispersal area ($A$) plays a crucial role in this process, as it determines the probability of finding colonizable vacant sites.…
The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work we study population survival or extinction using a stochastic, discrete…
An integro-differential equation on a tree graph is used to model the evolution and spatial distribution of a population of organisms in a river network. Individual organisms become mobile at a constant rate, and disperse according to an…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…
A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. However, many species are…
We present a discrete-time model of a spatially structured population and explore the effects of coupling when the local dynamics contain a strong Allee effect and overcompensation. While an isolated population can exhibit only bistability…
Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where…
An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…
We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics include the Allee effect. We show that mixing between patches dramatically influences the…
We model sex-structured population dynamics to analyze pairwise competition between groups differing both genetically and culturally. A sex-ratio allele is expressed in the heterogametic sex only, so that assumptions of Fisher's analysis do…
We investigate invasions from a biological reservoir to an initially empty, heterogeneous habitat in the presence of advection. The habitat consists of a periodic alternation of favorable and unfavorable patches. In the latter the…
This paper is devoted to the study of the persistence versus extinction of species in the reaction-diffusion equation: \begin{equation} u_t-\Delta u=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\in\Omega,\nonumber \end{equation} where $\Omega$ is of…
The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate…
'Evolutionary rescue' is the potential for evolution to enable population persistence in a changing environment. Even with eventual rescue, evolutionary time lags can cause the population size to temporarily fall below a threshold…
The Allee effect is an important phenomenon in population biology characterized by positive density dependence, that is a positive correlation between population density and individual fitness. However, the effect is not well studied in…
In this paper we consider a simple two patch reaction diffusion model with strong Allee effect, sufficiently distinct carrying capacities, similar reaction strengths, and strong diffusion. In the homogeneous case, i.e., in in the case of…
This paper is concerned with existence, non-existence and uniqueness of positive (coexistence) steady states to a predator-prey system with density-dependent dispersal. To overcome the analytical obstacle caused by the cross-diffusion…